What are the ups-and-downs of firearms when used in a zombie plague? There is no question that firearms are deadly. If you've ever brought a gun to a knife fight, chances are you are probably going to win.
One of the obvious problems with firearms is that they run out of ammunition. Each firearm has its own specific caliber of ammunition and once you run out of that caliber, if you cannot scrounge or buy any more, your shotgun essentially becomes a stick and not even a very good one at that. The real problem with firearms is that there are exceedingly loud. In a catastrophic zombie plague, the world would be a very quiet place. People would be lying low, not wanting to make any noise. If you use a shotgun or any sort of firearm to eliminate the zombie threat in front of you, you might as well stand on the roof with a dinner bell alerting any other zombie or hostile human within an earshot that you're there.
Imagine hoards of zombies, or starving people, even, in a city and they hear a gunshot. Everyone is going to go straight to that sound because where there are firearms there are probably other vital supplies and other people. The last thing you want to do is draw attention to yourself. Firearms should only be used as a last resort.
Other range weapons that are not so loud are the bow and arrow or a crossbow. A problem with both of those is that they also run out of ammunition and new ammunition is hard to create. You can't just whittle an arrow in your spare time, normally. Crossbows and compound bows like this often are very hard to load. It takes a lot of strength to actually pull them back. If you are going to use a bow, you want to use a very basic simple U bow. The real advantage of range weapons like firearms or bows is that you don't have to get close to your enemy. What you do not want to do is get within grabbing, biting range, of a zombie. Other basic range weapons are a brick or a stone. Whatever you can use to create distance and keep yourself from coming in direct contact with zombies, that's what you want to do.